Langmuir 1994,10, 870-876
870
Interpretation of Adsorption Isotherms at Above-Critical Temperatures Using a Modified Micropore Filling Model H. K. Shethna and S. K. Bhatia' Department of Chemical Engineering, Indian Institute of Technology, Powai, Bombay 400 076, India Received September 13, 1993. I n Final Form: January 3,1994"
A new micropore filling model, which has a Henry's law region and predicts an upper limit to micropore size, is applied here to adsorption at supercritical temperatures. Data obtained here on the adsorption of methane and carbon dioxide on activated carbons are interpreted in terms of this model, while utilizing independently obtained pore size distributions. The results show that the contributions of micropore filling and mesopore surface adsorption can vary considerably with temperature as well as adsorbate, because of the dependency of the upper limit of micropore size in which filling occurs on these variables. In light of these findings it appears that concepts such as micropore volume and mesopore surface area are not reliable characteristics of the pore structure as they vary with process conditions.
Introduction It is well established14 that adsorption in the fine micropores comprising activated carbons and zeolites occurs by a pore filling mechanism which is distinct from the surface layering process characterizing the larger mesopores. In the latter case the adsorption is most conveniently modeled by the classical Langmuir equation at above-critical temperatures, since only monolayer coverage is anticipated under such conditions. However, use of this model for microporous carbons often produces anomalously high surface area estimates,' indicating the need for adifferent kind of interpretation for the micropore filling process. The classicalDubinin-Radushkevich (DR) models and its extension due to Dubinin and Astakhov? the DA model, are the most widely accepted among the pore filling isotherms and have been applied over a wide range of temperatures, both below and above the adsorbate critical temperature.lI2 However, a well-known weakness of these models is the absence of a Henry's law limit at low pressures, suggesting their inapplicability in this region. This thermodynamic inconsistency at low pressures has prompted some researchers1 to consider the Dubinin model obscure, and others' to use more empirical alternatives. Nevertheless, the Dubinin approach is generally believed to be in the right direction, as in small pores overlapping potentials of opposing surfaces may be expected to yield enhanced adsorption, leading to the pore filling process envisaged in the model. On the other hand, in the mesopores, where there is negligible overlapping of the force fields, only monolayer adsorption is anticipated above critical temperatures since in this case adsorbateadsorbate interaction is relatively weak. The specification of the upper limit of micropore size in which the volume filling occurs is therefore a major concern in the modeling,
* To whom correspondence may be addressed. Abstract published in Aduance ACS Abstracts, February 15, 1994. (1) Gregg,5.G.; Sing, K. 5.W. Adsorption, Surface Area and Porosity; Academic Press: New York, 1982. (2) Yang, R. T. Gas Separation by Adsorption Processes; Butterworths: Boston, 1987. (3) Jaroniec, M.; Madey, R. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, 1988. (4) Rudzinsky, W.; Everett, D. H. Adsorption of Gases on Heterogeneous Surfaces; Academic Press: London, 1992. (5) Dubinin, M. M.: Raduehkevich, L. V. Dokl. Akad. Nauk SSSR 1947,55, 327. (6) Dubinin, M. M.; Aetakhov, V. A. Adu. Chem. 1971, 102, 69. (7) Sircar, S.Carbon 1987,25, 39. Q
but is not addressed in the classical DR and DA approaches. Consequently researchers have either chosen this limiting size empirically on the basis of ad-hoc assumptions7 or ignored this limit altogethefigby assuming a fillingprocess in the entire size region (0, m). As a standard a value of 20 A for the slit width has been suggested by IUPAC,l-' although this value is somewhat arbitrary as it may vary with the system as well as temperature. The above deficiencies of the classical theories have, however, been largely overcome in a recent development10 which considerably extends the scope of the pore filling model. One of the goals of that work was to correct for the absence of a Henry's law limit at low pressures by introducing a Langmuirian model in this region. With an increase in pressure a transition to the DA model is made at a critical coverage at which the slopes of the two isotherms are matched, a procedure which is thermodynamically consistent in that the heats of adsorption in both regions also match at the point of transition. A rather attractive feature of the analysis is that it also yields an upper limit to the micropore size for which such matching is possible, suggesting that this represents the limiting size for thermodynamic consistency,and therefore validity, of the pore filling model. In support of the new theory it was foundlothat the predictions were consistent with the large amount of published literature on the point of hysteresis closure which may be interpreted as the point of transition from a micropore fillingto a mesopore surface layering and capillary condensation mechanism. It may be noted that in a somewhat different development the Dubinin model has also recently been extended" to incorporate a Henry's law limit. However, the analysis did not yield an upper limit of pore size for the validity of the approach so that this part of the issue remains unresolved. At the same time the analysis introduces an additional parameter. Since the choice of this upper limit is important in isotherm interpretation, particularly for structural characterization, the alternative discussed above appears more attractive. In that work10 we reported the pore structure characterization of two commercial activated carbons using the new theory to interpret the corresponding isotherms for carbon dioxide at 195K. In the present work we report the isotherms for (8) Jaroniec, M.; Lu, X.; Madey, R. Langmuir 1989,5, 839.
(9) Wojsz, R.; Rozwadowski, M. Adsorpt. Sci. Technol. 1988, 6, 65. (10) Bhatia, S.K.;Shethna, H. K. Langmuir, submitted for publication. (11) Sundaram, M.Langmuir 1993,9,1568.
0743-7463/94/2410-0870$04.50/00 1994 American Chemical Society
Langmuir, Vol. 10, No. 3, 1984 871
Adsorption Isotherms at Above-Critical Temperatures
methane and carbon dioxide on these carbons at abovecritical temperatures, and discuss the interpretation in terms of the new theory and the pore size distributions presented earlier.
Theory For the primarily above-criticaltemperatures of interest in the present work, it is assumed that pore filling occurs in the micropores below a critical size (half-width), rm, and monolayer surface coverage occurs in the mesopores larger than this size. Since our study is concerned with activated carbon adsorbents, we consider slitlike pores, as is established to be the case for such materials.lJ2 For any micopore of half-width r we use the DA model
only above an adsorbate pressure Pc (Le., for P L P,),while for P < Pc we apply a Langmuirian form
in which B(r,P,T) is the fractional filling in the micropore. Upon equating the values of B and the isotherm slopes ( W a p ) at the transition pressure P,, we obtain10
(4)
where Q(r,T) is the solution to the nonlinear equation
Thus, the Langmuir parameter K and the unknown P, are related to the Dubinin parameters E&), 8, and n. Here E&) is the characteristic energy for a pore of half-width r, known to be given with sufficientaccuracy by the inverse relation13
with k = 12 (kJ.nm)/gmol. The parameter 0 is an affinity coefficient which varies with adsorbate, and has the value of unity for benzene. Equations 1-5 form the micropore filling model suggested recently,1°which can be used with any arbitrary form for Eo(r) as in eq 6. As mentioned earlier the approach has the attractive feature of continuity of the heat of adsorption at the transition pressure P,. A further remarkable outcome is that eqs 5 and 6 have no solution for r larger than a limiting value rmsatisfying
/3k nRT(1+ Qm)[ln((l+Qm)/Qm)l"+l)/" where
Qm
Q,ln(
-)
l+Qm Qm
=n-1 n
Thus, the above value of rmforms the upper limit of pore size (slit half-width) for which the Dubinin pore filling model can be made consistent with the existence of a lowpressure Henry's law region by interfacing with the Langmuir model. Since the latter is a thermodynamic requirement, the value of rm can be considered to specify the upper limit of pore size for which the pore filling model is valid. For pores above this size the conventional surface layering process applies. For above-critical temperatures where monolayer coverage is anticipated,
in which B, is the fractional surface coverage and KLthe corresponding Langmuirian equilibrium constant following
where -AH is the heat of surface adsorption in the monolayer. A further unknown in the above formulation is the pressure PO. Sufficiently below the critical temperature where the adsorbate-adsorbate interaction is strong, this is expected to be closely approximated by the saturation vapor pressure. However, near the critical temperature, and above it, this interaction is weak and adsorbateadsorbent interactionsdominatethe pore filling process. Consequently the value of POis difficult to estimate a priori under these conditions, and ita value must depend on the adsorbent surface characteristics as well as molecular properties of the adsorbent and adsorbate. Several attempts at approximating POin terms of bulk adsorbate properties only have been made in the past, as summarized by Yang;2 however, there is little agreement among the expressions which are based on empiricism and intuitive appeal. For the present purpose therefore we consider the general form
Po= Po"exp(-L/RT)
(11)
in which PO"and L are unknown constants. In the micropore filling model discussed above it may be noted that at any pressure P there exists a critical pore size r,(P) demarcating those pores undergoing filling by the Dubinin model and those filling by a Langmuirian model. This critical size is given by the inversion of Pc(rc>= P
(12)
where Pc(r)is given by eq 3, and Dubinin filling occurs for r < r,, while Langmuir filling occurs for r, < r < r,. For pores larger than rm surface adsorption occurs. Figure 1 depicts these processes in various regions of the pore size distribution. Following the related work,1° the overall adsorption isotherm at any pressure is given by
(7)
is the solution to
(12) Rodriguez-Reinoso,F.; Unares-Solano, A. In Chemistry and PhY8iC8 of Carbon; Thrower, P. A., Ed.; Marcell Dekker: New York, 1988: VOl. 21. (13)SGckli, H. F.; Kraehenbuehl, F.; Ballerini, L.; Bernardini, S. De. Carbon 1989,27, 126.
Here u is the molecular diameter of the adsorbate taken as its Lennard-Jones size parameter, NO is Avogadro's
Shethna and Bhatia
872 Langmuir, Vol. 10, No.3, 1994 0.04
,
I
1
7 0.03 O-5
E
sE
dr d€
0.02
L
k
: v
pore size, r
0.00 0
Figure 1. Adsorption regimes in different pore size ranges.
number, and C, is the molar amount adsorbed per unit mass of adsorbent. Further M is the molecular weight of the adsorbate and a, its molecular area, given by2 a, = 1.091(M/Ng)2/3
20
40
slit width, W
60
80
(i)
Figure 2. Pore size distribution of Active Carbon Indiagranules. 0.035
0.030
(14)
with the density p corresponding to that of the adsorbate liquid a t its normal boiling point. In the micropores it is known12 that the adsorbate molecules are in a compressed state, and we assume the density to be given bylo
0.01
T
‘7
Eb
0.025
A 0.020
E0
L
it 0.015 3
with the molecular area a d given by eq 14,but with p replaced by the density at the freezing point pf. This method was found to give values of pr in agreement with molecular simulation results for nitrogen adsorption,14and with known estimates12 for carbon dioxide adsorption in activated carbons.
Experimental Section
As an application of the model discussed above for abovecritical temperatures, experiments at atmospheric pressure were done with the adsorption of methane and carbon dioxide on activated carbon in the temperature range of 298-398 K. The adsorption was monitored on a DuPont Model 951 thermogravimetric analyzer (TGA) using helium as a carrier gas. All gases were of high purity (>99.9%),and the activated carbons were the same two commercialvarieties used in the related work. One was a granular activated carbon (grade ACG-60) manufactured by Active Carbon India Ltd.,and the other was an extruded variety of the NORIT type. The pore size distributions of these carbons had previously been determined10using carbon dioxide at 195 K, and are depicted in Figures 2 and 3. For the adsorption, gae flows into the TGA were controlled by means of Brooks Model 5860E electronic mass flow controllers. The balance housing of the TGA was continuously purged with 15 mL of helium/min, while a gas mixture of suitably chosen composition entered through the side arm of the furnace tube. All gas streams were passed through silica gel beds for drying, before passing through the mass flow controllers. About 30-35 mg of activated carbon sample, spread uniformly over the sample boat was used in each experiment. Initially the sample was degassed at 523 K under a helium stream of 60mL/min flow rate, for about 3 h. After this period, the total helium flow rate was raised to 200 mL/min and the sample cooled to the desired adsorption temperature. Care was taken to minimize moisture (14)Aukett, P. N.; Quirke, N.; Riddiford, 5.;Tenniaon, S. R.Carbon
1992, 30, 913.
30.010 U
0.005
0.000 0
20
40
60
a0
slit width, W (i) Figure 3. Pore size distribution of NORIT extrudates. ingress and leaks which are known to plague such experiments. On reaching and stabilizingat the desired temperature the helium stream entering the furnace tube was adjusted to one premixed with a chosen level of the adsorbate (CHI or COz). The total flow rate was maintained at 200 mL/min in all cases. When equilibrium was reached, and the sample weight was constant, the gas stream was again adjusted to one of a chosen higher adsorbate concentration and a new equilibrium attained. The equilibrium data so obtained were corrected for buoyancy effecta independently determined from blank runs, at the same temperature, in which adsorption did not occur.
Results and Discussion
Experimental Isotherms, Figures 4-7 depict the adsorption data obtained by the above procedure, for methane and carbon dioxide on the activated carbons. In these figures the abscissa represents the adsorbate partial pressure in the gas mixture with helium, which is assumed to be the same as the adsorbate pressure in the absence of the inert carrier. This latter assumption is supported by the observations of Gray,’6 who has reported that his earlier C02 adsorption equilibrium datalewith the NORIT extrudates, obtained thermogravimetricallyusing helium (15)Gray, P. G. Personal communication, 1993. (16) Gray, P. G.; Do, D. D. AZChE J. 1991,37,1027.
Adsorption Isotherms at Above-Critical Temperatures
Langmuir, Vol. 10, No. 3, 1994 873
1 .o
2
s
I
298.15 K 308.15 K 318.15 K A 333.15 K 4 343.15 K
:E
u
L
I
I
I
300
400
500
600
303.15 K 323.15K m 343.15 K A 363.15 K 0
0
T
0.8
Q
I
I
Q
.u
T
1.6 -
0.6
El
0
t,
22
0.4
0
4d
s
*
0.2
:*
0.0
0
100
200
300
400
500
600
700
pressure, P (mm Hg) Figure 4. Methane adsorption isotherms for Active Carbon India granules. Symbols represent experimental data and solid lines the present model fits.
-
,
1.0
I
0 T
$ 1 L)
I
I
A
I
298.15K 318.15K 333.15 K 343.15 K
I
I
I
fi
0
100
T
s2
1.80
I
Y
I
0 7
0)
1.35A
E
0.6
200
700
pressure, P (mm H g ) Figure6. Carbon dioxideadsorption isotherms for Active Carbon India granules. Symbols represent experimental data and solid lines the present model fits.
4
L
I
I
I
I
400
500
600
303.15 K 323.15 K 348.15 K 373.15 K 398.15 K
t,
0
100
200
300
400
500
600
700
pressure, P (mm H g ) Figure 5. Methane adsorption isotherms for NORIT extrudates. Symbolsrepresent experimentaldata and solid lines the present model fits.
as the carrier gas, were subsequently reproduced in a vacuum adsorption apparatus in which no carrier was involved. Further, at the same temperature, our own C02 data for the extrudates were also seen to be consistent with those of Gray and validating our results. Data Interpretation. For modeling the isotherms depicted in Figures 4-7, the conventional and simplest option is to use a straightforward Langmuirian model in eqs 9 and 10 since under supercritical conditions only monolayer coverage is anticipated. However, it was evident from the nonlinear nature of the usual transformed plots, an example of which is shown in Figure 8 for CHr on the granular activated carbon, that this model is not adequate for adsorptionon the microporous materials used. The curvature seen in this figure was evident in all the other cases as well, with the deviation from linearity being strongest at low pressures. Some scatter at low pressures is also noted in Figure 8, which is due to experimental errors. Nevertheless, the need for a different model is apparent. Use of an integrated Langmuir or Dubinin model also was not successful and yielded inconsistent results for the different adsorbates used. In the former
0
100
200
300
700
pressure, P (mm Hg) Figure 7. Carbon dioxide adsorption isotherms for NORIT extrudates. Symbolsrepresent experimental data and solid linea the present model fits.
case we used the recent formulation of Bhatia and subsequently extended by Bhatia,lE of the form (16)
Here ro is the minimum slit half-width and r, a most probable value. The above expressionfor K(r)is suggested by the observation' that the adsorption energy is inversely proportional to pore size and approaches a constant flatsurface value for large pores. The model thus haa the five (17) Bhatie, S. K.;Do,D.D.ROC. R. SOC.London A 1991,434,317. (18) Bhatia, S. K.ROC. R. SOC. London, eubmittad for publication.
Shethna and Bhatia
874 Langmuir, Vol. 10, No. 3, 1994
Table 1. Pore Size Distribution Constants carbon Active Carbon
1200
India aranules
constant ~~~
1000
ro (A)
ra (A) a1 (cm3/g)
d
a2
800
(cm3/(gA))
a3 (cmY(pA2)) x
Q,
a4 (cmV(pA3)) x
10'
I@
3.076 9.396 2.3397 -0.2233 9.0082 2.5356
NORIT extrudatee 2.973 10.464 1.9712 -0.1566 6.1393 1.2630
Table 2. Physical Property Values Used for Isotherm Fits
600
property 400
1
- / 0
100
200
300
400
500
600
700
pressure, P (mm Hg)
coz CH4
1.18 0.425
1.07 0.44
3.996 3.822
0.3939 0.3548
used to minimize the residual
Figure 8. Transformed isotherm plot for methane adsorption on Active Carbon India granules. Symbols represent experimental data and solid lines the present model calculations. constants KO,-AH, a, ro, and r, that were fitted for each set. In the case of the integrated Dubinin model we used the four-constant overall isotherm
with f ( r ) = $(r) and PO= hT 2, where h is a constant for a given adsorbate. This expression for PO has been suggested in the literature18 for supercritical conditions. However, both eqs 16 and 19 yielded inconsistent results for the carbon dioxide and methane isotherms on the same carbon, with the pore volumes differing by a factor of more than 2. Similar behavior was also found when eq 11was used along with eq 19 instead of Po = hT 2, increasing the number of constants to five. It may also be noted that while such heterogeneous isotherm models are increasingly being suggested in the literature,14 they do not allow for an upper limit to the pore size for filling, and are therefore incomplete. Consequently they do not consider the multilayer adsorption and capillary condensation process at low temperatures that are important in characterizing the larger pores. As a result of these considerations the approach suggested here, which has incorporated all these features,lo was adopted in the present study. At the low pressures involved in the experiments the amount of adsorption is considerably smaller than that required for saturation, so that it is not feasible to accurately extract pore size distributions using the model proposed here. This is because under these conditions the adsorption is expected to be dominated by the small pores and the model predictions are unlikely to be sensitive to the distribution of larger pores. Further, since for supercritical temperatures capillary condensation does not occur, the distribution of pores larger than rm cannot be obtained from the data. A more justifiable option is therefore to fit the model proposed here in eqs 1-15, using the pore size distributions depicted in Figures 2 and 3 which were obtainedlO from the C02 isotherms at 195 K. In this case the only unknowns are the constants KOand -AH in eq 10, related to the Langmuirian equilibrium constant in the mesopores, as well as the quantities PO" and L in eq 11, related to the value of POapplicable in the micropores. In fitting the isotherm data by the present approach, the Harwell Mathematical Library subroutine VAlOA was
which represents the sum of the squared errors. Here MI represents the number of adsorbate partial pressures and M Zthe number of temperatures at which the data for a given system were taken. Further, Caij represents the measured amount adsorbed at pressuref'i and temperature Tj, and C,(Pi,Tj) is its predicted counterpart. For accurately calculating the integrals in eq 13, a finite element quadrature was used, similar to that detailed in Bhatia and Chakraborty.19 All computations were done on aPC/ AT-486 microcomputer. For the calculations a value of n = 2.08 was used for each carbon, based on the earlier estimate.10 This determination was made from the observation that the lower closure point of hysteresis for nitrogen adsorption a t 77.4 K occurred at PIP, = 0.46 for each carbon, where P,is the saturation vapor pressure. This allowed calculation of rm, using a modified Kelvin model, assuming the point of hysteresis closure to correspond to the transition from continuous filling to a discrete condensation mechanism. Equations 7 and 8 could then be used to estimate n from the value of rm,and this was obtained as 2.08. In addition to n the pore size distributions for the two carbons, obtained earlier,1° and presented in Figures 2 and 3, were also used. These distributions, while plotted in terms of slit width W (=2r), represent converged results consistent with the general form
with $(r) being expressed by the Rayleigh form in eq 18. A total of four terms in the expansion (Le., N = 4) were found sufficient for convergence when fitting C02 isotherms at 195 K.l0 Table 1lists the values of the various constants in eqs 18 and 21 for each carbon. It may be noted that for both carbons the minimum slit width exceeds the value of the Lennard-Jones size parameter for each adsorptive used, so that all pores are accessible and f ( r ) = 0 for (u/2) I r I ro in the first integral in eq 13. Table 2 lists the values of the Lennard-Jones size parameter and other physical constants for each adsorptive which were used in the fitting. The values of the affinity parameter (19) Bhatia, S. K.; Chakraborty, D. MChE J. 1992,38,868.
Langmuir, Vol. 10, No. 3, 1994 875
Adsorption Isotherms at Above-Critical Temperatures 1 .o
Table 3. Fitted Parameter Values constant
K ~ 107 X -AH p0o x 1w L carbon adsorbate (mmHg-9 (kJ/mol) (mmHg) (kJ/mol) Activecarbon COz 6.685 8.882 5.243 7.541 Indiagrandee Cg 7.282 7.051 1.165 2.074 NORIT COz 0.304 16.878 9.877 8.831 extrudates CHI 1.838 10.819 8.891 7.261
-2
3 -
0.8
L
0.6
b,
?E
bU
were obtained by assuming proportionality with the parachor value20 and p = 1 for benzene. The solid lines in Figures 4-7 show the model calculations, indicating the ability of the model to fit the data. This is also evident from the typical transformed plot in Figure 8, where the solid lines representing the model results reproduce the experimental nonlinearity. Table 3 gives the values of the fitting constants PO', L , KO,and -AH for each case. It may be noted that for the supercritical conditions encountered here (except for the lowest temperature used for C02, which is only slightly lower than its critical value of 304.1 K)the parameters K L and POare more strongly determined by the adsorbateadsorbent interactions than the adsorbate-adsorbate interactions. Hence, the associated temperature coefficients are not expected to correlate with the latent heats of the adsorbates, though they are within about 30450% of the latter (except for CH4 on the granular activated carbon). Indeed, because of variation in surface energetic characteristics among the carbons, the constants fitted may be expected to vary, as is observed here. The present interpretation therefore has an advantage over the molecular modeling or simulation based appro ache^'^^^^ which use standard adsorption data for a reference nonporous carbon to determine adsorbate-adsorbent interaction parameters. Since the reference carbon is likely to have different surface characteristics, it may be expected that this influences the pore size distributions subsequently extracted. Clear evidence of this is seen in the work of Aukett et al.,14who found that the pore size distribution estimated by them for their carbon, using the molecular simulation approach for nitrogen adsorption data, was not adequate in describing methane adsorption on the same carbon. Consequently they reduced the pore volume by 20% in order to better approximate the methane data. A more justifiable approach would be to fit the interaction parameters for the required carbon in each case. However, this is currently impractical because of enormous computational requirements. The current approach, being phenomenological, is computationally much less intensive and is able to account for the surface characteristics of the carbon of interest by directly fitting the constants related to K L and PO.An assumption in the present approach is that the value of the exponent n is constant and independent of temperature as well as adsorbate. Clearly this is likely to be an approximation that needs to be verified by hysteresis experiments with several adsorbates on the same carbon. Contribution of Micropore Filling and Mesopore Surface Adsorption. Although much literature exists on adsorption under supercritical conditions,lv2J2 the use of pore size distributions in interpreting the data has hitherto received very little attention. A particular advantage of the present approach is that it readily yields the contributionsof micropore fillingand mesopore surface adsorption in the overall isotherm. The former is given (20)Dubinin, M. M. In Chemistry and Physics of Carbon; Walker, P. L., Ed.; Marcel Dekker: New York, 1967;Vol. 2. (21)Seaton, N.A.; Walton, J. P. R. B.; Quirke, N. Carbon 1989,27, 853.
s
4d
0.4
*
0.2
$ Eu
0.0 ..
0
0
100
200
300
400
500
600
700
pressure, P (mm H g ) Figure 9. Computed distribution of amount adsorbed by micropore filling and mesopore surface adsorption for methane on Active Carbon India granules at 298.15 K. 0.6
1
I
I
I
I
I
1
100
200
300
400
500
600
700
..
0
pressure, P (mm Hg) Figure 10. Computed distribution of amount adsorbed by micropore filling and mesopore surface adsorption for methane on Active Carbon India Granules at 318.15 K.
by the sum of the first two terms and the latter by the third term, on the right-hand side of eq 13. Figures 9 and 10 illustrate these predicted contributions for CH4 adsorption on the granular carbon, at the lowest and highest temperatures used (Le., 298.15and 343.15K),respectively. In both these figures the solid curve represents the predicted overall isotherm, while the dotted curve represents the contribution of micropore fillingand the dashed curve that of mesopore surface adsorption. The linearity of the latter in both cases is consistent with the low pressures used and indicates that Henry's law holds for the mesopores. At the lower temperature of 298.15 K, micropore filling provides a significantly larger contribution than surface adsorption in the pressure range used. However, at the higher temperature of 343.15K the two mechanisms are equally significant, with the latter providing a larger contribution above a gas-phase methane pressure of about 550 mmHg. This behavior with temperature is to be expected in view of a decrease in rmwith an increase in temperature as indicated by eq 7. Table 4 provides the variation with temperature of the estimated values of rm and the corresponding micropore volume undergoing filling, as well as the mesopore surface area
876 Langmuir, Vol. 10, No. 3, 1994
Shethna and Bhatia
Table 4. Variation of Micropore Volume and Mesopore Surface Area carbon adsorbate Activecarbon Cop India granules CHI
NORIT extrudates
coz
C&
temperature r
(K)
(&
303.15 323.15 343.15 363.15 298.15 308.15 318.15 333.15 343.15 303.15 323.15 348.15 373.15 398.15 298.15 318.15 333.15 343.15
5.73 5.38 5.06 4.79 5.25 5.08 4.92 4.70 4.56 5.73 5.38 4.99 4.66 4.36 5.25 4.92 4.70 4.56
micropore mesopore volume area (cmYa) (m%) 0.111 0.087 0.067 0.052 0.079
0.068 0.059 0.047
0.040 0.082
0.064 0.047 0.034 0.024 0.058 0.439 0.035 0.030
455 498 535 568 513 534 553 578 593 453 485 518 546
568 496 524 542 553
for each case. The significantvariation of these quantities with temperature and adsorbate is an indication of the futility of characterizinga porous material by ita micropore volume and mesopore-cum-macropore surface area as is the common practice. The complete pore size distribution is perhaps the only consistent and reliable characteristic of the pore structure.
Summary
A new model for supercriticaladsorption on microporous adsorbents, accountingfor micropore filling and mesopore surface adsorption, is proposed here. The model utilizes independently determined pore size distributions, and is applied to the interpretation of methane and carbon dioxide isotherms obtained here on microporous carbons. The results show that the upper limit of pore size for micropore fillingvaries significantlywith temperature and adsorbate. Consequently the micropore volume in which filling occurs, and the mesopore surface area on which surface adsorption occurs,can also vary significantly. These findings indicate that parameters such as pore volume and mesopore surface area, being variable quantities, are not reliable characteristics. A more useful characterization is therefore offered by the complete pore size distribution. The present model is also computationally simpler than the recent molecular model approaches, and can account for variation in surface characteristics among different carbons. Acknowledgment. This research has been supported by a grant [No. 111.4(39)/90-ETIfrom the Department of Science and Technology. The authors acknowledge the assistance of Mr. D. N. Jaguste and Mr. A. Mairal in the initial stages of the experimental work.
